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not be on the same straight line, and in many cases are not. When the whiffletree is exactly perpendicular to the direction of the forces, it is obvious that the two forward forces must be equal if the arms are equal, or in inverse ratio to the arm lengths, if the latter are not equal. If the whiffletree is inclined, the case is not so obvious. It is proposed in this experiment to test out the effect of inclination when the load is attached in front of, on, and back of the line joining the points of application of the two forward forces.






Fig. 2.

Suspend two spring balances from a cross-bar above the table. A special board is provided with holes bored as indicated in Fig. 2. Long nails can be thrust through the holes and wire loops placed over the nails so that the board can be suspended from the spring balances and a load from the center of the bar. A line is drawn across the center of the board perpendicular to the axis and other lines are drawn at angles of 10°, 20°, and 30° with this line.

(a) Suspend a load of at least 2 kgm at the center and place the end supports in the holes marked 3-3. Record readings of the balances with the bar horizontal, and when inclined at angles of 10°, 20°, and 30°, being sure in every case that the balances are hanging vertically and the wire loops are not rubbing on the board. Does the inclination have any noticeable effect on the relative magnitudes of the two forces?

(b) Repeat the tests with the balances fastened to the holes 1-1, and 2-2 in turn. In this case is there a change in the

relative magnitudes of the forces with inclination? In an actual case would the forward horse have to pull more or less than the other?

(c) Repeat the tests with the balances fastened to the holes 4-4, and 5-5 in turn. In this case would the forward horse have to pull more, or less?

(d) Fasten the left-hand balance to hole 3 and the righthand one to hole 6. Take the readings of the balances with the bar horizontal. Measure the lengths of the arms and compare the arm ratio with the inverse force ratio. What would be the proper arrangement to use for a three-horse team?

Explain why cases (a), (b), and (c) work out as they do. Look up in your text-book the exact definition of moment-arm. Does inclination of the bar change the actual length of the moment-arms? Does the inclination change both arms alike in all cases? Draw carefully diagrams to illustrate cases (a), (b), and (c) and use them in the explanations asked for.



References: Stewart, Physics, Sect. 28-34; Kimball, College Physics, Sect. 176, 182, 185; Duff, College Physics, Sect. 118-119; Spinney, Text-Book of Physics, Sect. 106, 111,


(a) Suspend a metal cylinder from one arm of a balance and determine its weight in air. Then place a beaker of water on a suitable support so that the cylinder hangs freely in the water and find its weight in water. Find the difference between these two results. According to Archimedes' principle, this loss of weight equals the weight of the displaced water. Measure the cylinder with vernier calipers, calculate its volume and the weight of the water it must displace, remembering that one cubic centimeter of water weighs one gram. Do the results agree? Find the specific gravity of the metal.

(b) Weigh in air a body which is lighter than water, e. g., a piece of paraffin. Use the cylinder of part (a) for a sinker. Its weight in water has already been determined. Tie the paraffin and sinker together and find the weight when the two

are hanging freely in water. From the sum of the weights of the paraffin in air and the sinker in water, subtract the weight of the combination in water. This gives the buoyant force on the paraffin or, by Archimedes' principle, the weight of water it displaces. Find the specific gravity of the paraffin.

(c) Weigh a closed glass tube loaded with mercury or shot, first in air, then in water, and finally in a solution of copper sulfate or any other liquid to be tested. Calculate the loss of weight of the tube when placed in water and when immersed in the solution. From these data determine the specific gravity of the solution.

(d) An inverted Y-tube is used. To the middle branch is attached a short rubber tube, with a pinch-cock and mouth-piece. The two arms are dipped into beakers, one containing water and one containing copper-sulfate. By suction applied at the middle tube, the liquids can be caused to rise in the arms. (For sanitary reasons the student is advised to wash the mouth-piece before putting it into his mouth.) A meter-rod is arranged to slide along each arm so that the height may be read. The lower end of each meter-rod is cut off and a glass rod inserted of such a length that the point comes just at the zero of the rod. Each rod should therefore be lowered till the glass point just touches the surface, before reading the height of the column. Since the atmospheric-pressure on the surface in each beaker is the same, and the pressure at the top of each column is the same, the pressure due to each column must be the same. Therefore,

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The specific gravity of water is 1. Make six determinations with columns of different heights.



References: Stewart, Physics, Sect. 31; Kimball, College Physics, Sect. 182, 186; Duff, College Physics, Sect. 119; Spinney, Text-Book of Physics, Sect. 111.

Determination of the specific gravity of a body requires a knowledge of the weight of the body and the weight of an equal

volume of water. The specific gravity bottle or pyknometer is a small flask, usually of 50 or 100 cubic centimeters capacity, fitted with a ground-glass stopper through which there is a capillary tube. For special purposes they are made in various shapes. If no such bottle is available, a small flask with a line etched about its neck may be used. The common laboratory balance is not sensitive enough to permit accurate work with pyknometers of small capacity; one capable of weighing exactly to hundredths of a gram at least is necessary.

Any deposits on the interior of the bottle should be removed with suitable cleaning solution, then the bottle must be washed, rinsed out with alcohol and thoroughly dried inside and out. A current of air from an aspirator will assist greatly in drying the interior. Be sure that no liquid remains in the tube through the stopper before placing the pyknometer on the balance to find the weight of the empty bottle. When filling the pyknometer introduce enough liquid to fill the bottle part way up the neck, press the stopper gently into place and wipe off the excess liquid forced out through the capillary tube. After removing each liquid, wash the bottle and stopper and dry thoroughly, if accurate results are desired.

In testing solids, the materials must be in small pieces and free from water. Shot, metal pellets, glass beads, pieces of broken porcelain, and sand are materials suitable to use. The method described is used in soils laboratories for finding the specific gravities of soils. The student may save time by planning the work so that all dry weighings may be made before putting any liquids into the bottle.

The following weighings should be made in finding the specific gravities of liquids and solids, but they need not be made in the order specified.

1. Pyknometer dry and empty

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(P + W)

(P + L) (PS)

(P + S + U )

5. Containing solid and distilled water to fill

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It should be obvious how to find the weight of any contained liquid and of an equal volume of water from weighings 1, 2, and

3, and from the values to compute the specific gravities of the liquids.

The weight of the solid is easily found from 1 and 4. The weight of water displaced by the solid is equal to (WU) and can be determined from weighings 1, 2, 4, and 5. Then the specific gravity of the solid can be found.



References: Stewart, Physics, Sect. 39, 45; Kimball, College Physics, Sect. 191, 199; Duff, College Physics, Sect. 126, 127; Spinney, Text-Book of Physics, Sect. 117, 122.

To study the relation between the pressure and volume of a mass of air at a constant temperature. Air is contained in a closed, graduated glass tube, which is connected by heavy rubber tubing to an open glass tube containing mercury. This open tube can be raised and lowered, so that the height of the mercury in the graduated tube may be varied. The pressure of the air in the graduated tube is equal to the atmospheric pressurewhich is found by reading the barometer-plus the pressure due to the excess height of mercury in the reservoir over that in the graduated tube. If the mercury in the closed tube is higher than that in the reservoir tube, the difference in levels must be subtracted from the barometer reading. The barometer should be read at the beginning of the experiment and once or twice more during the period, especially if it is changing at all rapidly. Use each reading in the calculations until the next one is taken, but do not use the average. The volume of the air may be read directly from the scale etched on the tube. In some types of apparatus for this experiment, the tube containing the gas is not graduated. In such cases the actual volume of the gas need not be found, but the length of the gas column above the mercury in the closed tube may be used in its place. Obviously the volumes will be proportional to the lengths of the gas column, if the tube is of uniform bore.

First set the tubes so that the mercury is at the same level, in both of them and so that the closed tube is somewhat less

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